{"id":"https://openalex.org/W2048361500","doi":"https://doi.org/10.1007/s00500-011-0755-7","title":"A modified learning algorithm for the multilayer neural network with multi-valued neurons based on the complex QR decomposition","display_name":"A modified learning algorithm for the multilayer neural network with multi-valued neurons based on the complex QR decomposition","publication_year":2011,"publication_date":"2011-08-20","ids":{"openalex":"https://openalex.org/W2048361500","doi":"https://doi.org/10.1007/s00500-011-0755-7","mag":"2048361500"},"language":"en","primary_location":{"id":"doi:10.1007/s00500-011-0755-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00500-011-0755-7","pdf_url":null,"source":{"id":"https://openalex.org/S65753830","display_name":"Soft Computing","issn_l":"1432-7643","issn":["1432-7643","1433-7479"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Soft Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052101553","display_name":"Igor Aizenberg","orcid":"https://orcid.org/0000-0002-5994-6568"},"institutions":[{"id":"https://openalex.org/I51380931","display_name":"Texas A&M University \u2013 Texarkana","ror":"https://ror.org/01x3z9745","country_code":"US","type":"education","lineage":["https://openalex.org/I51380931"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Igor Aizenberg","raw_affiliation_strings":["Texas A&M University-Texarkana, 7101 University Ave., Texarkana, TX, 75503, USA","Texas A&M University-Texarkana, 7101 University Ave., 75503, Texarkana, TX, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Texas A&M University-Texarkana, 7101 University Ave., Texarkana, TX, 75503, USA","institution_ids":["https://openalex.org/I51380931"]},{"raw_affiliation_string":"Texas A&M University-Texarkana, 7101 University Ave., 75503, Texarkana, TX, USA#TAB#","institution_ids":["https://openalex.org/I51380931"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008924460","display_name":"Antonio Luchetta","orcid":"https://orcid.org/0000-0003-4319-1495"},"institutions":[{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Antonio Luchetta","raw_affiliation_strings":["Department of Electronics and Telecommunications, University of Florence, Via S. Marta 3, 50139, Florence, Italy","University of Florence, Department of Electronics and Telecommunications, Via S. Marta 3, 50139 Florence, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Electronics and Telecommunications, University of Florence, Via S. Marta 3, 50139, Florence, Italy","institution_ids":["https://openalex.org/I45084792"]},{"raw_affiliation_string":"University of Florence, Department of Electronics and Telecommunications, Via S. Marta 3, 50139 Florence, Italy","institution_ids":["https://openalex.org/I45084792"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007810132","display_name":"S. Manetti","orcid":"https://orcid.org/0000-0002-5798-7147"},"institutions":[{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Stefano Manetti","raw_affiliation_strings":["Department of Electronics and Telecommunications, University of Florence, Via S. Marta 3, 50139, Florence, Italy","University of Florence, Department of Electronics and Telecommunications, Via S. Marta 3, 50139 Florence, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Electronics and Telecommunications, University of Florence, Via S. Marta 3, 50139, Florence, Italy","institution_ids":["https://openalex.org/I45084792"]},{"raw_affiliation_string":"University of Florence, Department of Electronics and Telecommunications, Via S. Marta 3, 50139 Florence, Italy","institution_ids":["https://openalex.org/I45084792"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5052101553"],"corresponding_institution_ids":["https://openalex.org/I51380931"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":3.1061,"has_fulltext":false,"cited_by_count":56,"citation_normalized_percentile":{"value":0.91970575,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"16","issue":"4","first_page":"563","last_page":"575"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10876","display_name":"Fault Detection and Control Systems","score":0.9778000116348267,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.7376154065132141},{"id":"https://openalex.org/keywords/backpropagation","display_name":"Backpropagation","score":0.6743764281272888},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6599217653274536},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.64715975522995},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6328983306884766},{"id":"https://openalex.org/keywords/qr-decomposition","display_name":"QR decomposition","score":0.5964189171791077},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5082611441612244},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.48222315311431885},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4040970206260681},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.24816355109214783}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.7376154065132141},{"id":"https://openalex.org/C155032097","wikidata":"https://www.wikidata.org/wiki/Q798503","display_name":"Backpropagation","level":3,"score":0.6743764281272888},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6599217653274536},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.64715975522995},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6328983306884766},{"id":"https://openalex.org/C188060507","wikidata":"https://www.wikidata.org/wiki/Q653242","display_name":"QR decomposition","level":3,"score":0.5964189171791077},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5082611441612244},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.48222315311431885},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4040970206260681},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.24816355109214783},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00500-011-0755-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00500-011-0755-7","pdf_url":null,"source":{"id":"https://openalex.org/S65753830","display_name":"Soft Computing","issn_l":"1432-7643","issn":["1432-7643","1433-7479"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Soft Computing","raw_type":"journal-article"},{"id":"pmh:oai:flore.unifi.it:2158/559094","is_oa":false,"landing_page_url":"http://hdl.handle.net/2158/559094","pdf_url":null,"source":{"id":"https://openalex.org/S4306402033","display_name":"Florence Research (University of Florence)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45084792","host_organization_name":"University of Florence","host_organization_lineage":["https://openalex.org/I45084792"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W142384176","https://openalex.org/W639538290","https://openalex.org/W1576347883","https://openalex.org/W1585539754","https://openalex.org/W1594058661","https://openalex.org/W1894035673","https://openalex.org/W1981745143","https://openalex.org/W1999558486","https://openalex.org/W2019848683","https://openalex.org/W2025855399","https://openalex.org/W2047515252","https://openalex.org/W2063648366","https://openalex.org/W2075148278","https://openalex.org/W2075665712","https://openalex.org/W2082130524","https://openalex.org/W2088259102","https://openalex.org/W2092590148","https://openalex.org/W2094631910","https://openalex.org/W2104870463","https://openalex.org/W2105050785","https://openalex.org/W2107190265","https://openalex.org/W2116621978","https://openalex.org/W2124776405","https://openalex.org/W2125789994","https://openalex.org/W2126944419","https://openalex.org/W2136892987","https://openalex.org/W2146287682","https://openalex.org/W2150159007","https://openalex.org/W2150671991","https://openalex.org/W2158243843","https://openalex.org/W2161694749","https://openalex.org/W2161780063","https://openalex.org/W2166074449","https://openalex.org/W2167039992","https://openalex.org/W2167766297","https://openalex.org/W2169578168","https://openalex.org/W2289891913","https://openalex.org/W2313953460","https://openalex.org/W2314485382","https://openalex.org/W2476841360","https://openalex.org/W2487295360","https://openalex.org/W2798909945","https://openalex.org/W3013533083","https://openalex.org/W3207342693","https://openalex.org/W4229539396","https://openalex.org/W4248510537","https://openalex.org/W4292692317","https://openalex.org/W4300402905"],"related_works":["https://openalex.org/W4239286941","https://openalex.org/W2088845016","https://openalex.org/W589102260","https://openalex.org/W1966421350","https://openalex.org/W1485846902","https://openalex.org/W3037218165","https://openalex.org/W1868434454","https://openalex.org/W4366985237","https://openalex.org/W4367365565","https://openalex.org/W2128396103"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}